The gambit system basically means they can program monsters with specific behaviours that they will then automatically use. This is better than the current method of scripting each mobs with a specific set of commands that trigger at specific times. This should make things LESS predictable.
Example:
Ifrit could be programmed with the following "gambits"
Enemy weak to fire : Radiant Plume
HP < 30% : Hellfire
HP = 50% : Crimson Cyclone
Nearest target : Sear :
Target with highest Enmity : Attack
Basically (in theory) this could help make fights less based on timing by having sets of moves set to fire at specific triggers, and less on a schedule. Preventing "swipe swipe skills, but forcing players to have to be ready for skills.
Think of combinations like "Enemy status = Protect : dispelga" and you start to get the picture. It worked really well in XII to create powerful characters that could automatically use a variety of skills autonomously.
Edit: it seems a few of us have chimed in =) I was distracted typing.
Oh and Chocobo Gambit system = amazing.
I hope path companions are the same way!
